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**On the asymptotic optimum allocation in estimating inequality from complete data.**
*(English)*
Zbl 0771.62083

Summary: Studies dealing with the quantification of inequality of a population with respect to a given quantitative attribute, provide us with a large class of measures. Among these, we can distinguish, because of their properties and operativeness, the ones coinciding with, or being ordinally equivalent to, the dimensionless “additively decomposable inequality indices”.

As indicated in previous papers, many populations, whose inequality in relation with an attribute is useful to quantify, are too large to be censused but large samples from them can be drawn and they arise naturally stratified. On the basis of these last two advantages, we will approach the optimum allocation in estimating inequality, and a comparison with the proportional allocation, and with the absence of strata, will be later established.

As indicated in previous papers, many populations, whose inequality in relation with an attribute is useful to quantify, are too large to be censused but large samples from them can be drawn and they arise naturally stratified. On the basis of these last two advantages, we will approach the optimum allocation in estimating inequality, and a comparison with the proportional allocation, and with the absence of strata, will be later established.

### MSC:

62P20 | Applications of statistics to economics |

62D05 | Sampling theory, sample surveys |

91B82 | Statistical methods; economic indices and measures |

### Keywords:

stratified sampling; additively decomposable inequality indices; quantification of inequality of a population; optimum allocation
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\textit{M. A. Gil} and \textit{I. Martínez}, Kybernetika 28, No. 4, 325--332 (1992; Zbl 0771.62083)

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